NATIONAL BANK OF BELGIUM

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1 NATIONAL BANK OF BELGIUM WORKING PAPERS - DOCUMENT SERIES STOCK MARKET VALUATION IN THE UNITED STATES Parick Bisciari (*) Alain Durré (**) Alain Nyssens (***) The views expressed in his paper are hose of he auhors and do no necessarily reflec he views of he Naional Bank of Belgium, nor of he European Cenral Bank. We would like o hank Marcia De Wacher, John Fell, Philippe Jeanfils and Quenin Wibau for heir very valuable commens and suggesions for improving his paper. We would also like o hank he people who provided us wih heir excellen help or assisance, especially our NBB colleagues from Financial Markes, he Inernaional Cooperaion and Financial Sabiliy, he Saisics and he General Secrearia, and also from he Secrearia of he Research Deparmen. All errors are our own. (*) (**) (***) NBB, Research Deparmen, ( parick.bisciari@nbb.be). NBB, Research Deparmen, ( alain.durre@nbb.be). NBB, Research Deparmen, ( alain.nyssens@nbb.be). NBB WORKING PAPER No NOVEMBER

2 Ediorial Direcor Jan Smes, Member of he Board of Direcors of he Naional Bank of Belgium Saemen of purpose: The purpose of hese working papers is o promoe he circulaion of research resuls (Research Series) and analyical sudies (Documens Series) made wihin he Naional Bank of Belgium or presened by exernal economiss in seminars, conferences and convenions organised by he Bank. The aim is herefore o provide a plaform for discussion. The opinions expressed are sricly hose of he auhors and do no necessarily reflec he views of he Naional Bank of Belgium. The Working Papers are available on he Bank's websie : hp:// Individual copies are also available on reques o: NATIONAL BANK OF BELGIUM Documenaion Service boulevard de Berlaimon 14 B Brussels Imprin: Responsibiliy according o Belgian law: Jean Hilgers, Member of he Board of Direcors, Naional Bank of Belgium. Copyrigh Naional Bank of Belgium Reproducion for educaional and non-commercial purposes is permied provided ha he source is acknowledged. ISSN: X 2 NBB WORKING PAPER No NOVEMBER 2003

3 Absrac This paper gives an overview of some issues relaed o marke valuaion, focusing on he developmens on he New York equiy markes. The 42.4 p.c. fall in he S&P 500 price index beween 24 March when i reached is all-ime high - and 31 December 2002 is siuaed in a very long erm perspecive. I hen appears ha some bear markes were more pronounced in he pas bu ha he bull marke preceding he bear marke had been paricularly long and impressive in exen. Given his sharp correcion, we will discuss wheher he S&P 500 was correcly valued a he end of To his end, we make use of valuaion indicaors defined as he raio of he price o a fundamenal. The fundamenals considered here are, according o he discoun dividend model, annual earnings and, according o Q-heory, ne worh. In December 2002, price-earnings (P/E) sill showed a significan overvaluaion of equiy prices when compared o he hisorical average over he period bu, since July 2002, he overvaluaion has no been significan in he case of Q. The evidence is even more mixed when he comparison is made, for each valuaion indicaor, wih heir average over he las 10 years. Simulaions based on VAR models for P/E and Q were carried ou o check wheher, on wo occasions, he S&P 500 in real erms climbed o a level perceived as irraional given pas experience, implying ha a correcion had o be expeced. These occasions were he so-called 1929 and 2000 bubbles. The models showed ha, a some poin in ime before he peak in (real) sock prices was reached, he real S&P 500 exceeded he upper band of he 95 p.c. confidence inervals during boh periods. For each of hem, he Q model showed earlier and more persisen signals of significan overvaluaion of sock prices han for he P/E model. Finally, in December 2002, boh models indicaed ha he sock price had come back largely wihin he confidence inerval. NBB WORKING PAPER No NOVEMBER

4 TABLE OF CONTENTS INTRODUCTION RECENT AND HISTORICAL EVOLUTION OF THE S&P ARE STOCK PRICES PREDICTABLE? VALUATION INDICATORS Theories underlying he fundamenal o be compared wih sock prices Discoun Dividend Model Q-heory Daa Earnings Q Descripive analysis An iniial look a he valuaion of sock prices Do he valuaion indicaors send he righ signal abou sock marke prices? Are misalignmens in he valuaion indicaors correced by sock price changes? Empirical analysis Univariae and mulivariae analyses The models...43 Simulaion exercises...43 CONCLUSION...50 Annex 1 Tesing he random walk hypohesis...52 Annex 2 Derivaion of he Discoun Dividend Model...54 Annex 4 Migh an increase in earnings coninue o conribue, from now on, o a downward adjusmen in P/E?...58 Annex 5 The VECM Model...62 References...65 NBB WORKING PAPER No NOVEMBER

5

6 INTRODUCTION We ake an ineres in developmens in he American sock markes for hree reasons. Firs, in he Unied Saes, sock marke movemens influence boh household and business consumpion and invesmen o a greaer exen han in oher counries. Second, he New York Sock Exchange (NYSE) is he world s leading sock marke. The imporance of he New York marke is even greaer if we also ake accoun of he Naional Associaion of Securiies Dealers Auomaed Quoaion (NASDAQ) and he American Sock Exchange (AMEX). Third, movemens in sock marke prices in he euro area are correlaed wih hose observed in he Unied Saes. The S&P 500 reached an all-ime high on 24 March 2000 of 1, poins before plummeing by 42.4 p.c. o poins on he evening of 31 December The purpose of his paper is wofold: o place his even in a hisorical perspecive and o provide some answers o he quesion wheher, despie he sharp correcion which has already occurred, shares are sill overvalued and prices could herefore fall even furher. This paper aims o be accessible o a broad public. I is divided ino hree secions. Secion 1 commens on he recen developmen of he S&P 500 sock price index. The main feaures are a srong and more or less coninuous rise beween 1995 and 2000, and a sharp fall since he beginning of 2000, which allows he period as a whole o be considered as a financial bubble; hereafer called he "2000 bubble". The upward phase ("bull marke") had already sared in Augus In his paper, his movemen and he subsequen downward phase ("bear marke") are compared wih similar phases in he pas, especially in real erms. Finally, he parallel has been drawn beween he 2000 bubble and he one which occurred in Alhough some conclusions could be drawn from hese hisorical comparisons, one has o ake a more in deph look o fully undersand he curren valuaion of he sock marke. Secion 2 raises he quesion of he "random walk" hypohesis. According o he heory of efficien markes, sock marke prices are supposed o follow a random walk, and hus i is 1 Unless oherwise specified, all ime series daa presened in his aricle have 31 December 2002 as he cu-off dae on he basis of informaion available on 31 January NBB WORKING PAPER No NOVEMBER

7 impossible o predic heir fuure movemens. This hypohesis has been esed and is srongly rejeced. The rejecion of he random walk hypohesis implies ha sock prices can be forecased o a cerain exen. To his end, i is necessary o use insrumens which link he price of shares o a "fundamenal". Secion 3 is devoed o analysing hese valuaion indicaors. Two fundamenals are mainly examined: earnings and ne worh. The firs finds is jusificaion from he discoun dividend model, while he second comes from he Tobin's Q heory of invesmen. Afer a brief review of he key aspecs of hese heories, secion 3 conains a presenaion of he daa and a descripive analysis. This sars wih an iniial ouline of he curren valuaion of sock prices by comparing he laes observed daa for each of he valuaion indicaors wih heir hisorical average. We have also checked wheher, in he pas, he wo valuaion indicaors under review gave he correc signals regarding fuure movemen in sock prices, especially before he major urning poins. Finally, we examine wheher he exreme variaions of he valuaion indicaors were caused by changes in real sock prices or by changes in real fundamenals. Secion 3 ends wih a simulaion exercise based on VAR models. We have paricularly analysed, for he 1929 and he 2000 bubbles, wheher he sharp flucuaions in he sock price were compaible wih he evoluion of company earnings and ne worh. 2 NBB WORKING PAPER No NOVEMBER 2003

8 1. RECENT AND HISTORICAL EVOLUTION OF THE S&P 500 There are several sock markes operaing in he Unied Saes. The bes-known among hem are siuaed in New York; hese are, in decreasing order of size according o he sock marke capialisaion of he shares quoed on hem, he NYSE, he NASDAQ and he AMEX. The commens made in his aricle relae o he above-menioned markes and are confined o share ransacions. Over ime, some privae companies have developed indices enabling he general developmen of American sock markes o be assessed. These indices may differ from one o anoher according o crieria such as he mehod of weighing he index, he markes covered, he ype of companies, he number of companies, he breakdown beween markes and he relaive weigh given o he economic secors. In his paper, we focus 2 on he S&P 500 index. Since 1995, he S&P has experienced wo phases: an almos consan rise beween January 1995 and 24 March 2000, and a plunge down o a low poin reached on 9 Ocober A rebound followed unil 28 November bu he index declined again somewha in December. 2 3 There are oher sock price indices which cover he American markes. In decreasing order of marke capialisaion (as a he end of June 2002), hese indices are he Wilshire 5000, he Thomson Financial Daasream oal marke, he S&P 500, he Dow Jones Indusrial Average (DJIA) and he Nasdaq Composie. We give preference o he S&P 500 index mainly because i is he reference index for porfolio managemen and is he only one of hese indices for which here are monhly hisorical series, boh for prices and for oher series which are useful for our research (dividends, earnings, ), going back as far as The availabiliy of such long series is a considerable asse for empirical, saisical and above all economeric work. Oher reasons, no specific o he S&P 500, jusify ha we have recourse o i: he price evoluion of his index, ogeher wih ha of he Thomson Financial Daasream's oal marke index, is he mos closely correlaed o ha of he broades sock price index, he Wilshire The S&P 500 is also broadly represenaive of he American sock markes: a he end of June 2002, is marke value represened 78 p.c. of ha of he Wilshire Finally, unlike he DJIA, i is weighed by sock marke capialisaion. Throughou he paper, we shall focus on he price variaions of he indices as our main concern is sock marke valuaion. Neverheless, an invesor also pays aenion o dividends as hey are par of he reurn. NBB WORKING PAPER No NOVEMBER

9 Char 1 - S&P 500 sock price index since 1995 (Index 2 January 1995 = 100) Source: Thomson Financial Daasream. Beween January 1995 and March 2000, he S&P 500 had jus over ripled in value. This imporan progression of he index led many analyss o qualify i, in rerospec, as a bubble. Consequenly, he index showed a sharp correcion. I wen down 49.1 p.c. o he low reached on 9 Ocober A he end of he period, he price index sill showed a subsanial increase since January This recen evoluion of he S&P 500 can be placed in a long-erm perspecive as, whereas he S&P 500 was no acually inroduced unil 1928, in he 1930s he Cowles Commission 4 made i possible o reconsiue a hisorical monhly series going back o he year Cowles and Associaes (1939). The daa is made available by Professor Rober J. Shiller on he Universiy of Yale websie: hp:\\aida.econ.yale.edu\~shiller\daa.hm. Whereas daa has exised since 1871, i has been shown since 1872 for graphical reasons. 4 NBB WORKING PAPER No NOVEMBER 2003

10 Char 2 - S&P 500: movemen since 1872 (index = 10, log scale) Sources: Shiller's websie (see foonoe 5), Thomson Financial Daasream. A graph of his index since 1872 on a logarihmic scale (char 2) shows ha: over a very long period, he index of sock marke prices has risen subsanially; sock prices declined on several occasions. The sharpes correcion was observed beween Sepember 1929 and June The foregoing analysis suffers from he disadvanage of no aking accoun of he movemen in consumer prices. The shareholder is keen o proec himself agains he erosion of he purchasing power of his porfolio caused by he general rise in prices. Some sylised facs can be esablished on he basis of a real 6 erms series (char 3): sock prices show a seep upward rend; 6 In his paper, real erms series always refer o nominal series deflaed by he consumer price index (indices = 100). NBB WORKING PAPER No NOVEMBER

11 afer World War I, sock prices significanly exceeded he sraigh rend line during hree sub-periods: around 1929, in he 1960s and from he mid-1980s onwards; he upward deviaion compared o he rend in 1929 was followed by he sharpes correcion ever observed; prices having subsequenly remained well below he rend unil he end of he 1950s; he upward deviaion compared o he rend observed during he 1960s led o a correcion in he 1970s, especially in 1973 and 1974; finally, despie he correcion in progress since 2000, prices were sill, in December 2002, appreciably above he rend. Even more serious: never, during previous periods characerised by a posiive deviaion, had his been so grea. Char 3 - S&P 500: movemen since 1872 (in real erms 1, log scale) Sources: BLS, Shiller's websie (see foonoe 5), Thomson Financial Daasream; own calculaions. 1 Deflaed by he consumer price index (indices = 100). In he res of he secion an aemp has been made o synhesise he main upward and downward periods of sock marke prices, referred o by financial specialiss as "bull" and "bear" markes respecively. As our analysis relaes o he long erm, aenion will be paid 6 NBB WORKING PAPER No NOVEMBER 2003

12 o he variaions calculaed on he basis of monhly averages raher han daily daa. Table 1 refers o sock prices in nominal erms. Table 1 - "Bear markes" 1 a leas as significan as he 1987 crash Sar of he period (peak) Dae of he lowes poin Value a he lowes poin (indices peak = 100) Number of monhs beween peak and lowes poin End of period (dae of reurn o original value) Number of monhs beween he lowes poin and he reurn o original value May 1872 June February June 1881 Augus December Sepember 1902 Ocober March Sepember 1906 November Augus December 1909 Augus January Sepember 1929 June November December 1968 June March January 1973 December July Augus 1987 December July Augus 2000 December (28) - - Sources: Shiller's websie (see foonoe 5), Thomson Financial Daasream; own calculaions. 1 Based on he S&P 500; sock prices in nominal erms. The mos recen of he significan sock marke correcions which preceded laes developmens is ha of he so-called crash of Ocober In Augus 1987 he S&P 500 had peaked. Following a pronounced decline, alhough i lased only four monhs, he S&P had los (in December 1987) 26.8 p.c. of is Augus value, and i ook alogeher 19 monhs before he index recovered is iniial value. Since 1871, he S&P 500 has shown nine oher falls as large as ha of he auumn of The occurrence of a sock marke crash or "bear marke" is herefore no a all excepional in iself, despie he above-menioned rising rend. Table 1 also shows oher 7 The sock marke crashes aken ino accoun here correspond o he following crieria: we have recourse consanly o he S&P 500 index (previously named Cowles index); he sar of he period is a hisorical peak in he series of he S&P 500 in nominal erms; we consider sock price declines as large as he 1987 crash; we impose no ime resricion in our definiion of a sock marke crash. Mishkin and Whie (2002) also used wha hey qualify as he "universally agreed" sock marke crashes of Ocober 1929 and Ocober 1987 as benchmarks for heir procedure o idenify sock marke crashes. Their procedure differs from ours on wha hey refer o as key facors, namely he choice of sock marke index, he size of he collapse and he imeframe of he decline. More explicily, hey used he DJIA for 1903 o 1940 and hey shifed o he S&P 500 in 1946; hey considered sock price declines of over 20 p.c.; and hey looked a declines over five differen ime window s (one day, five days, one monh, hree monhs and one year). NBB WORKING PAPER No NOVEMBER

13 lessons: he laes crash is characerised by a fall of around 40 p.c. in he S&P 500 beween Augus 2000 and December The correcion is herefore already greaer han ha of he auumn of 1987 and han several oher periods (noably December June 1970); more significan declines han he curren one have been observed only in four previous periods. In hree of hese ( , and ), he maximum fall was however no more han 50 p.c. Following he Ocober 1929 crash, on he oher hand, he fall of S&P 500 down o is lowes poin (in June 1932) reached 84.8 p.c. and i ook a lile over 22 years for he index o reurn o is original value. This was in November 1958; he downward phase of he nine previous bear marke periods (since 1871) had lased on average 54 monhs (abou four and a half years). During hese same periods i ook on average 60 monhs (five years) for prices o reurn o heir iniial level. In December 2002, he presen period began only 28 monhs ago. In char 4, comparison has been made beween he presen correcion and cerain super bear marke periods, i.e. cases of bear markes enailing a correcion of a size a leas equivalen in real erms o ha of he presen one. 8 NBB WORKING PAPER No NOVEMBER 2003

14 Char 4 - "Super Bear markes" 1 (in real erms, indices peak = 100) Monhs from he peak Sep Sep Sep Nov Dec Jan Aug Dec.2002 Sources: BLS, Shiller's websie (see foonoe 5), Thomson Financial Daasream; own calculaions. 1 Based on he S&P 500. Since 1871, only hree oher super bear marke periods have been idenified: Sepember 1906-Sepember 1928, Sepember 1929-November 1958 and December 1968-January These periods are longer han hose considered in he analysis carried ou in nominal erms: as consumer prices end o increase over ime, i akes longer for he S&P 500 o reurn o he iniial level. As a resul, some super bear marke periods in real erms cover several bear marke periods in nominal erms, so ha he laer are more numerous han he former 8. The fall in he S&P 500 observed since Augus 2000 follows a course close o ha of he hree preceding super bear markes in real erms. If he curren period coninues in a similar manner, i may be feared ha he rough has no ye been reached, and he periods required o enable he index o reach is lowes poin and hen reurn o is preceding peak migh be very long. Firs, a he low poins of December 1920, June 1932 and July 1982, 8 By way of example, he srong inflaion of he 1970s did no allow he S&P 500 o reain is December 1968 level in real erms unil January 1992, whereas i had reached his level again in nominal erms by March Also, he super bear marke in real erms of he period comprises hree bear markes displayed by he analysis in nominal erms ( , and 1987). NBB WORKING PAPER No NOVEMBER

15 he S&P 500 had los, respecively, 70, 80.6 and 63.6 p.c. of he real value which i had reached when i was a is previous peak, agains barely 42.2 p.c. beween Augus 2000 and December Second, he minimum had been reached afer over 14 years, nearly 3 years and over 13 years respecively in he preceding periods whereas in December 2002 a lile over 2 years passed since Augus Third, in he hree preceding periods, a long furher period - respecively a lile over 5 years, a lile over 26 years and nearly 8 years - had elapsed before he S&P 500 reurned o is iniial volume. Consequenly, he oal duraion of he hree above menioned super bear markes had been respecively 22 years, a lile over 29 years and a lile over 23 years. Char 5 - "Bull markes" (in real erms, indices low = 100) Monhs from he low June 1877-Sep.1906 Dec Sep June 1932-Dec July 1982-Aug Source: Shiller's websie (see foonoe 5); own calculaions. We also need o ake a look a significan rises in he S&P 500, he so called bull markes. Char 5 is devoed o a comparison, also in real erms, beween he las bull marke and he previous ones. No crierion of he exen of he rise in he sock price index is used o define he bull markes. We merely ake he rough 9 of he super bear markes as heir saring dae and heir subsequen peaks as he end dae. 9 The rough for he firs bull marke corresponds o he minimum of he real S&P 500 reached in June NBB WORKING PAPER No NOVEMBER 2003

16 The cumulaive rise of he S&P 500 beween he las low poin in real erms, observed in July 1982, and he peak reached in Augus 2000 had been considerable as he index was muliplied by nearly eigh. The bull marke of he 1920s had been wice as shor, and he real sock marke price had been muliplied by only five. Oher bull markes, on he oher hand, were longer. This was he case wih he periods exending, on he one hand, beween June 1877 and Sepember 1906 and, on he oher hand, beween June 1932 and December During he laer period, he real value of he S&P 500 had been muliplied by more han eigh. The bull markes considered in char 5 ended, more ofen han no, in a more or less long phase of sock marke euphoria, generally coinciding wih srong expecaions of high fuure profis hanks o he spread of new echnologies: railway and elegraph companies in , auomobile, elecrical, radio and cinema indusries in , "nify-fify" 10 companies such as he high-ech firms IBM and Xerox, as well as high-profile consumer producs firms such as Coca-Cola and McDonald's in he 1950s and 1960s and, finally, he companies emblemaic of he informaion and communicaion echnologies (ICT) during he second half of he 1990s. The sock marke correcions which followed hese phases of euphoria can be explained by a downward revision of fuure profis. For example, during he firs of hese super bear markes, he appearance on he scene of wo echnologies compeing wih railways, namely mass producion of moor cars and rucks, led o he bankrupcy of he main American railway companies by To conclude, he sock marke correcion observed beween Augus 2000 and December 2002 is by no means excepional eiher in is lengh or in is exen. However, he preceding upward movemen of prices had been paricularly long and impressive in exen. I is very emping oday o compare he "bubble of 2000 o ha of As he choice of saring dae migh have an effec on he conclusions which migh be drawn from his comparison, we consider wo differen crieria o se i: he previous exreme low poin 11 for he real price (char 6) and he momen when he sock valuaion deviaes from is hisorical average, which is esimaed a around 15 for he price-earnings raio 12 (char 7) This is a lis of 50 nify companies for which he marke had high expecaions a ha ime and ha raded a very high price-earnings raios (Shiller, 2000). Siegel (1998) repored average price-earnings (P/E) of 41.9 for hese 50 socks a heir marke peak in 1972 ha he compared wih an average P/E of 18.9 for he S&P 500 index. This corresponds o he saring poin of he bull markes represened in char 5. We shall review his concep in more deph in secion 3 and show ha he hisorical geomerical average of he P/E proved o be slighly below 15, i.e NBB WORKING PAPER No NOVEMBER

17 Char 6 - Comparison beween he 1929 and 2000 bubbles (in real erms, indices low 1 = 100) Monhs from he low Dec June 1932 July March 2003 Sources: BLS, Shiller's websie (see foonoe 5), Thomson Financial Daasream; own calculaions. 1 The saring dae is deermined as he momen when he previous exreme low poin for he real price has been reached. Char 7 - Comparison beween he 1929 and 2000 bubbles (in real erms, indices low 1 = 100) Monhs from he low Oc June 1932 Jan Dec Sources: BLS, Shiller's websie (see foonoe 5), Thomson Financial Daasream; own calculaions. 1 Defined here by he las monh when he price-earnings raio was lower han NBB WORKING PAPER No NOVEMBER 2003

18 From chars 6 and 7, we conclude ha: - while he rise in real prices was faser a he ime of he 1929 bubble, i was also far less impressive; - in December 2002, real prices were sill far above he iniial level, whaever crieria are used for choosing he saring dae. In June 1932, he correcion brough real prices back o heir iniial level should he saring dae be assumed o be he previous exreme low poin reached in December 1920 and even barely half of heir iniial level if he las monh during which he price-earnings raio was under 15, ha is Ocober 1927, is referred o. NBB WORKING PAPER No NOVEMBER

19 2. ARE STOCK PRICES PREDICTABLE? According o he Efficien Markes Hypohesis (EMH) in finance, fuure sock prices canno be prediced. As Samuelson (1965) saes i, "in an informaionally efficien marke, asse price changes mus be unforecasable if hey are properly anicipaed, i.e., if hey fully incorporae he expecaions and informaion of all marke paricipans". In oher words, "a marke in which prices always fully reflec available informaion is called efficien" (Fama, 1970). The quesion of he (un)predicabiliy of sock prices in finance is closely relaed o he random walk hypohesis. Indeed, if sock prices follow a random walk, hen hey are unforecasable by definiion. To illusrae his purpose, ake for insance he case where sock prices, P, are explained by he following equaion: P = µ + ρ 1 + ε (1) P where µ is a consan, called drif parameer, ρ he esimaed auoregressive coefficien and ε is he innovaion erm or shock 13. If sock prices follow a random walk, i involves ha ρ = 1 and he incremens, ε, mus be whie noise. Tha means ha hey mus respec wo condiions: absence of auocorrelaion and absence of heeroskedasiciy 14. The mos imporan condiion requires ha incremens mus be uncorrelaed. Simply saed, if sock prices follow a random walk, his means ha equaion (1) is sufficien o explain he dynamics of P. Therefore, one of he mos direc and easies way o A shock symbolises new informaion available wihin he marke. Ideally, he incremens, ε, should be independenly and idenically disribued wih a zero-mean and a consan variance (see Annex 1). In oher words, he incremens, ε, do no have o be auocorrelaed and heeroskedasic. In he lieraure, hese condiions are ofen represened by he following expression: ε ~IID (0,σ 2 ). However, i is ofen recognized ha he assumpion of idenically disribued incremens may no be plausible for financial asse prices, especially over long ime spans. For example, over a wo-hundred-year sample period, many developmens (echnological progress, marke srucure, financial innovaion, ec.) may explain ime-variaion in volailiy of many financial prices. 14 NBB WORKING PAPER No NOVEMBER 2003

20 es he random walk hypohesis for he sock price is o check for auocorrelaion 15. Indeed, he presence of auocorrelaion in he incremens, ε, is mosly he sign of an omied explanaory variable and hus ha sock prices migh be predicable o some degree. The homoskedasiciy condiion, or non-heeroskedasiciy in he incremens, requires ha he variance of incremens is consan over ime. Since his variance is used for deermining he significance level of he explanaory variables, i.e. P 1 in equaion (1), his condiion warrans an unbiased analysis over he significan variables whaever he subsample considered. Acually, wih unsable variance, he explanaory variable p -1, for example, may be significanly differen from zero during some sub-periods bu no during oher sub-periods. We esed hese condiions for he monhly series of he S&P 500 over he sample period January 1871 o December The resuls we obained, deailed in Annex 1, confirm hose found recenly in empirical lieraure (Malkiel, 2003 and Shiller, 2003), i.e. a srong rejecion of he null hypohesis of no auocorrelaion and no heeroskedasiciy. Boh sandard auocorrelaion and heeroskedasiciy ess clearly sugges he problems of an omied variable and insabiliy of he variance in he incremens. Furhermore, according o he sabiliy of variance condiion, if he random walk hypohesis holds for socks reurns, heir variance should decrease linearly over ime, which also seems o be slighly rejeced. The rejecion of he random walk hypohesis, and hence he EMH, in pracice explains he emergence of heories, noably in macro-finance, relaing he sock price o a fundamenal. 15 The uni roo ess, which expliciely check if he coefficien ρ is significanly equal o one, are ofen confused wih ess of he random walk hypohesis. Of course, boh elemens are indirecly relaed as we will see in secion 3.4, bu, by consrucion, he uni roo ess are no designed o deec predicabiliy (Campbell e al., 1997, Chaper 2). NBB WORKING PAPER No NOVEMBER

21 3. VALUATION INDICATORS Given he rejecion of he random walk hypohesis, several sudies have hus emerged in lieraure in order o deec wha kind of variables may explain he flucuaions of he sock price, i.e. wha is (are) he fundamenal variable(s) of he sock price. Among poenial candidaes, he dividends or he earnings, relying on a firs heory (discoun dividend model) and he ne worh, relying on a second heory (Q-heory) are in general considered. 3.1 Theories underlying he fundamenal o be compared wih sock prices The discoun dividend model (DDM) relies on he idea ha a company has o generae earnings in order o expand in he fuure. As a resul, i posulaes ha he sock price is equal o he sum of all discouned dividends generaed by he sock. The Q-heory argues ha he equiy price of a company should reflec is balance shee value. The observed price may hen differ, someimes significanly, from he equilibrium price consruced by applying he hypoheses of he underlying heory. In ha case, we can conclude ha eiher he observed price is no jusified in he ligh of he heory, and ha a correcion is ineviable, or ha he hypoheses used for he valuaion are inappropriae (Wibau, 2000). Since we consider ha sock prices are mainly driven by he flucuaions of fundamenals, his implies ha any significan gap beween he curren sock prices and is heoreical value (considered as he equilibrium value of equiy) has o be viewed as a signal of a fuure correcion in prices Discoun Dividend Model A framework for predicing he sock prices is given by he DDM, which relaes he curren sock prices o he expeced discouned dividend in he long run. According o his, he heoreical value of a sock should herefore reflec he discouned sum of he fuure cash flows associaed wih he invesmen. These cash flows consis of dividends (i.e. he disribued par of earnings) and capial gains. Algebraically, he presen value of he sock price may hus be represened by he following equaion: 16 NBB WORKING PAPER No NOVEMBER 2003

22 P 1 D 1+ h h N i N e = + i P e + N i= 1 (2) where P is he curren sock price, e D is he expeced dividend (per share), e P is he expeced sock price and h is he discoun rae ha corresponds here o a consan reurn for an invesmen in socks covering he period from i o N. However, expecing socks reurns for long ime spans is no an easy ask, which is he bigges disadvanage of his framework. Neverheless, in he lae 1950s, his framework has received renewed ineres hanks o he resricions proposed by wo economiss. By posulaing perfec compeiion and perfec subsiuabiliy beween he various means of holding wealh, Gordon and Shapiro (1956) show ha heoreical sock prices may be reduced 16 o he following expression, which is called he "Gordon-Shapiro formula": P ( 1 + g ) D = (3) h g where D is he curren dividend (per share) and g is he assumed consan rae of growh of expeced dividends 17. This model makes he sock price exremely sensiive o a permanen change in h. The discoun facor h represens he opporuniy cos of he invesmen under consideraion. Moreover, he sock reurn, h, can be broken down as he reurn on a risk-free asse, r (which is ofen represened by he reurn yielded on a bond issued by a Sae wih a good credi raing), and an equiy risk premium relaed o he feaures of his ype of asse, σ. Therefore, equaion 3 becomes: P ( 1 + g) D = (4) r + s g By rearranging he model, i is possible o obain anoher expression of equaion (4): he dividend yield, DY defined as he raio of he dividend per share and he sock price: DY D = P r + σ g = (4') 1+ g A deailed descripion of he links beween he simple ne reurn on a sock and equaion (3) is given in Annex 2. Noe ha equaion (3) holds if, and only if, h>g. NBB WORKING PAPER No NOVEMBER

23 Moreover, when assuming ha a consan fracion δ of earnings (per share) E is paid ou as dividends, i.e. D = δe, we can obain from equaion (4) he price-earnings raio (or P/E); he raio of he sock price and he earnings per share: P E δ 1 = r + σ ( + g) where he erm δ is known as he payou raio. Since dividends are he disribued par of he earnings, Gordon-Shapiro's heory amouns o saing ha, in he long erm, sock g prices mus move in line wih fuure earnings anicipaed by he agens 18. (4'') In he remainder of he paper, we shall focus on he P/E as he DY proved o be a poor valuaion indicaor for he following reasons. The DY can give correc signals of over- or under-valuaion of sock prices when comparing is curren value o is hisorical average if and only if he pay-ou raio is consan over ime. If his is no he case, in pracice, invesors can sill ge decen reurns wih a low DY, as long as hey ge higher capial appreciaion. Therefore, he DY indicaor will be biased. As shown in Char 15, he pay-ou raio clearly poins ou a decreasing rend over ime. In he laer half of he wenieh cenury, companies paid ou lower dividends in relaion o heir earnings han in he pas (Smihers and Wrigh, 2001, Brav e al., 2003); undisribued earnings increase companies' ne worh and, hence, heir abiliy o pay addiional dividends in he fuure. Since value is made up of boh curren dividends and he capaciy for fuure growh, low DYs are no necessarily a sign of an overvalued sock marke. 18 Using his heoreical framework, many oher specificaions (or simplificaions) have been proposed in empirical lieraure. For example, one model posulaes ha sock price flucuaions are mainly explained by movemens in he difference beween he earnings yield and he long-run ineres rae. This model described in Lander e al. (1997) is ofen called he Fed model. The auhors use a simple error correcion model ha predics he reurn of he S&P based on he deviaions from a presumed equilibrium beween forecased earnings yield and yields on bonds. Weheril and Weeken (2002) show how his alernaive model is acually an exension of Gordon-Shapiro's heory. 18 NBB WORKING PAPER No NOVEMBER 2003

24 Char 8 - Payou raio: hisorical view Sources: Shiller's websie (see foonoe 5), S&P; own calculaions. Anoher disadvanage of he DY sems from he fac ha dividends are no he only fuure cash flows 19. For example, hese cash flows have increasingly been disribued in he form of share buy-backs, especially in recen years 20 (Brav e al., 2003). If a large par of cash flows is disribued o shareholders oherwise han via dividends, his makes he DY less useful as a summary saisic for valuaions Q-heory Average Q, formalised by Tobin (1969), is inended o capure he enire marke value of he company (including he marke value of deb) and compare i wih oal asses. I can be expressed as follows: This poin had already been made by Miller and Modigliani (1961) in heir seminal paper on sock valuaion, which saes ha he crucial series ha markes should be valuing is he oal flow of cash beween companies and shareholders, no simply dividends. The mos sriking shif happened in he 1980s and 1990s, when significan raes of share buy -backs implied ha ne new issues were negaive (Wrigh, 2002). NBB WORKING PAPER No NOVEMBER

25 Average Marke value of Equiies + Liabiliies Q = (5) Toal asses which is basically 21 he raio of he discouned value of a company's fuure earnings o he replacemen cos of is oal capial sock 22. By expressing average Q as he sum of he expecaions on fuure changes in he capial sock, he rae of profiabiliy (as capured by he raio beween dividends and capial), and fuure reurns, Roberson and Wrigh (2002) showed ha here is barely any evidence ha average Q predics invesmen, some evidence ha i predics fuure profiabiliy, bu srong evidence ha i predics fuure reurns. 3.2 Daa The subsecion is devoed o he descripion of he daase used hroughou he res of he paper. In paricular, we look a daa on earnings and on Q Earnings There are various ways of measuring earnings and mos of hem are subjec o biases. Two major sources of differences in esimaing earnings can be considered: differences in accouning conceps and differences in he esimaion period. As regard differences in he accouning conceps, as repored earnings are officially communicaed o he Securiies and Exchange Commission and audied in accordance wih he Generally Acceped Accouning Principles. They are more reliable han unaudied earnings such as operaing earnings and pro forma earnings (S&P, 2002). I is no surprise ha operaing earnings consanly exceeded as repored earnings, so ha P/E based on operaing earnings appeared lower and hus less worrying in recen years han P/E based on as repored earnings. As wih as repored earnings, some differences appear, depending on he daa providers. As regards differences in he esimaion period, some auhors resor o anicipaed earnings while ohers use observed earnings If average Q exceeds one, hen he company can increase earnings by invesing. Fixed capial is generally evaluaed a he marke price (financial concep) which can differ from he accouning concep. 20 NBB WORKING PAPER No NOVEMBER 2003

26 Among he laer caegory of auhors, some make heir analysis on he basis of earnings for he las year, ohers on he basis of smoohed earnings, i.e. earnings calculaed on he basis of an average of observaions over he las en years. This version has he advanage of smoohing ou flucuaions in earnings due o emporary evens and business cycles (Shen, 2000). Earnings end o be cyclical, bu a en-year period does no necessarily coincide wih he flucuaing duraion of cycles. Moreover, as real earnings end o increase over ime, average earnings over en years end o be lower han he earnings of he mos recen year, so ha P/Es calculaed on an average of earnings are usually higher han P/Es calculaed on las year's earnings. Auhors of he former caegory (Lander e al., 1997) sugges adoping forward earnings. The advanage of forward earnings is ha hese series remain closes o he behaviour of invesors who work ou heir invesmen sraegy on he basis of expecaions concerning he fuure behaviour of he markes. However, hese forward earnings are supposed o anicipae operaing earnings (which, hemselves, are no fully reliable; see supra) and hey end o be upward biased 23 (even when compared o las year's operaing earnings). Forward P/Es herefore end o give he false impression ha sock prices are cheaper han hey really are. The earnings per share (E 24 ) used in he paper are, according o Shiller (2000, op. ci.), he observed four-quarers railing 25 as repored earnings published by S&P. This daa is available on Shiller's websie Wadhwani (1999) and Panigirzoglou and Scammel (2002). 24 In he res of he paper, E shall sand for earnings per share. 25 For he monhs of March, June, Sepember and December, E is he sum of he earnings per share of he las four quarers. The E daa for he oher monhs is obained by linear inerpolaion. 26 See foonoe 5. NBB WORKING PAPER No NOVEMBER

27 3.2.2 Q Recourse o average Q as a predicor of fuure sock price movemens has been recenly underlined by Smihers and Wrigh (2001). These auhors propose anoher measure of Q which hey labelled as "equiy Q", defined as: Marke Value of Equiies Equiy Q = (6) Ne Worh This definiion is in line wih he raio published regularly in he company balance shees produced alongside he Federal Reserve's flow of funds accouns. These figures can be found on an annual and a quarerly basis for all quoed and unquoed non-financial companies. Equiy Q has he same properies, wih respec o he impac of changes in each of is componens, as average Q. Thus, a rise in he value of deb increases boh raios, oher hings being equal. A value of 1 for Equiy Q will also imply a value of 1 in average Q definiion. In our furher analysis, Equiy Q is preferred over average Q because his raio relaxes he srong assumpion according o which he marke value of a company is unaffeced by is mehod of financing 27 (Smihers and Wrigh, 2001). Anoher advanage of Equiy Q is ha i can be consruced wihou recourse o capial sock daa a marke prices, for which he availabiliy is far from easy (Wrigh, 2002). We can also express Equiy Q per share, so ha equaion (6) becomes: where NW sands for Ne Worh per share. P Equiy Q = (7) NW According o he heory, he mean value of Q, if we could measure i properly, should be precisely pariy (in he case of perfec compeiion) or somewha above (in he case of imperfec compeiion). As Smihers and Wrigh (2001) mainain, in a world of imperfec saisics, Equiy Q has an average below pariy. Lower mean values are explained by Wrigh (2002) by a sysemaic endency o over-esimae he replacemen value of he 27 This assumpion holds only under Miller-Modigliani condiions, in paricular he absence of company failures (Wrigh, 2002). 22 NBB WORKING PAPER No NOVEMBER 2003

28 physical capial sock, on accoun of he fac ha economic depreciaion may occur a a more rapid rae han recorded depreciaion. Pickford e al. (2002) consruced a monhly proxy for Q using S&P 500 daa. In his paper, his series will be referred o as Q. Conrary o Equiy Q, Q series herefore includes financial companies and is limied o he 500 companies comprised in he S&P 500 index. I makes i easy o compare Q wih P/E. In building his Q series, Pickford e al. (2002, op. ci.) assume ha he mis-measuremen of depreciaion discussed above has an imporan impac on aemps o derive he esimaed ne worh of US quoed companies from heir published reained earnings, bu ha he impac is relaively sable over ime. This mehod accordingly measures ne worh aking ino accoun an "average" degree of mis-saemen of earnings 28. Hence, recorded earnings were scaled down by an amoun ha makes Q equal o 1 on average. Besides he difficuly of measuring he rae of capial depreciaion, Q faces anoher well-known measuremen problem 29. Indeed, capial sock is no measured direcly: only he change in he capial sock can be measured. In he res of he paper, we have made use of he Q series available on he Smihers and Co websie 30 as of January The series ends on July 2002 (laes available daa) as we were no able o updae he daase buil by Smihers' eam Descripive analysis An iniial look a he valuaion of sock prices We can gain an iniial idea of he curren (and pas) valuaion of sock prices by considering he raios beween he curren sock price and he value of he corresponding fundamenal a a given momen (E or NW, depending on he case), and comparing hem wih heir hisorical average Pickford e al. (2002, op. ci.) furher claim ha i will no herefore make any allowance for he excepional mis-saemen of earnings ha has occurred in recen years. Deails of he mehod used for building he Q series are given in Pickford e al. (2002). These problems apply for Q daa in all counries, even in he Unied Saes. Ouside he Unied Saes, high qualiy ne worh saisics over a long period simply do no ye exis. For he Unied Kingdom, see Smihers and Wrigh (2001) and MacGorain and Thompson (2002). For Japan, see Ogawa and Kiasaka (1995) and Smihers and Wrigh (2001). hp:\\ Anoher way of approaching sock valuaion, in he case of he fundamenals used in Gordon-Shapiro s formula, is o compare he sock price wih he heoreical price resuling from equaion 4. This mehod, presened by Weheril and Weeken (2002), among ohers, requires esimaing he heoreical price based on assumpions regarding earnings growh (g) and he equiy risk premium (s). NBB WORKING PAPER No NOVEMBER

29 This approach has is disadvanages: he choice of he hisorical benchmark is acually no unconroversial. Some commenaors have argued ha hisorical relaionships may have broken down and ha long-erm averages - such as hose calculaed by Shiller since may herefore no longer be appropriae benchmarks (Weheril and Weeken, 2002, op. ci.). For pracical reasons, he aforemenioned approach has been used in he curren secion. We consider eiher upward or downward deviaions from he average as significan if hey exceed 25 p.c. in absolue value. a. Price-earnings Over he period as a whole, he P/E calculaed for socks in he S&P 500 averaged Char 9 - Price-earnings raio on he S&P 500: hisorical view Average Sources: Shiller's websie (see foonoe 5), S&P, Thomson Financial Daasream; own calculaions. The black hick horizonal lines represen a flucuaion margin of ± 25 p.c. Beween 1871 and 1995, whenever he P/E significanly exceeded is hisorical average (e.g., when i was higher han 20), correcions occurred sooner or laer; on each occasion, 24 NBB WORKING PAPER No NOVEMBER 2003

30 no only did he P/E rever o is mean, bu an over-reacion ensued, wih he P/E hen remaining below is hisorical value. Similarly, when he P/E fell subsanially shor of is hisorical average (e.g. by dropping below 10), i reurned sooner or laer o is long-erm average, hen over-reaced, someimes overshooing he average o a significan degree. Since 1995, he P/E has reached hisorical peaks, wih prices someimes reaching 47 imes E in March The P/E subsequenly dropped back o around 29 in December so ha he exen of he overvaluaion, as measured on he basis of a hisorical P/E, scaled back o 105 p.c. This value neverheless surpasses anyhing seen in he period. When Alan Greenspan 32 issued his warning abou he "irraional exuberance" of he sock markes in December 1996, prices sood a jus 19 imes E. b. Q Q is shown for he period January July 2002 period in char 10. The hisorical average is slighly 33 above 1. Q reached a peak in December 1999 which is far beyond he 25 p.c. upward bound, and a sharp correcion followed. In July 2002, he exen of overvaluaion as measured on he basis of Q, came back o around 25 p.c. above is mean. Char 10 - Q: hisorical view 3,0 2,5 2,0 1,5 1, Average 0,5 0, Source: Smihers and Co websie (see foonoe 30); own calculaions. The black hick horizonal lines represen a flucuaion margin of ± 25 p.c Greenspan (1996). The average is above 1, probably because he scaling down process ook place over a slighly shorer period. NBB WORKING PAPER No NOVEMBER

31 c. Firs conclusions on sock marke valuaion In he 1990s, whaever he fundamenal considered, boh valuaion raios moved subsanially away from heir long-erm averages, and such deviaions had never been ha large in he pas. This promped some commenaors o sugges ha equiy prices could no depar for much longer from heir hisorical relaionships wih he fundamenals and herefore needed o fall. In December 2002, he P/E sill showed a significan overvaluaion of equiy prices when compared o heir hisorical average, bu since July 2002 he overvaluaion was no ha imporan in he case of Q. The evidence is even more mixed if, for each valuaion indicaor, we compare he laes daa (hose from December 2002) wih heir average over he las en years insead of heir hisorical average. We migh hen conclude eiher ha he socks are no longer overvalued (on he basis of Q) or ha, hough sill overvalued, hey are much less overvalued (on he basis of P/E). Table 2 - Sensiiviy of he valuaion indicaors o he ime horizon chosen for he Indicaor average Value in December 2002 Average P/E Average Q Sources: Shiller's websie (see foonoe 5), Smihers and Co websie (see foonoe 30), S&P, Thomson Financial Daasream; own calculaions July 2002 (laes daa available). In he Gordon-Shapiro framework, a higher value for he average over he las en years han for he hisorical average can be jusified on he basis of equaions (4") (secion 3.1.1) by a lower equiy risk premium, a lower real risk-free ineres rae or a higher growh rae. This hird facor relaes o New Economy argumens ha expecaions of higher produciviy growh and oupu growh resuling from he increased usage of ICT suppored rapidly rising sock prices in he lae 1990s. Wih his reservaion in mind, we shall keep he average as he benchmark for he res of he aricle. 26 NBB WORKING PAPER No NOVEMBER 2003